MinT - Information on Result #1565115

Information on Result #1565115

Linear OOA(64⁸³, 114885, F₆₄, 3, 28) (dual of [(114885, 3), 344572, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁸³, 114885, F₆₄, 2, 28) (dual of [(114885, 2), 229687, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁸³, 131075, F₆₄, 2, 28) (dual of [(131075, 2), 262067, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁸³, 262150, F₆₄, 28) (dual of [262150, 262067, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁸³, 262151, F₆₄, 28) (dual of [262151, 262068, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(25) [i] based on
      1. linear OA(64⁸², 262144, F₆₄, 28) (dual of [262144, 262062, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(64⁷⁶, 262144, F₆₄, 26) (dual of [262144, 262068, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁸³, 22976, F₆₄, 33, 28) (dual of [(22976, 33), 758125, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row